Solve the system of equations.
–x+6y=13
4x–10y=–10
To solve the system of equations, we can use the method of substitution.
Step 1: Solve one of the equations for either variable. Let's solve equation 1 for x:
-x + 6y = 13
-x = -6y + 13
x = 6y - 13
Step 2: Substitute the expression for x in the second equation.
4x - 10y = -10
4(6y - 13) - 10y = -10
24y - 52 - 10y = -10
14y - 52 = -10
14y = 42
y = 3
Step 3: Substitute the value of y back into one of the original equations to find x. Let's use equation 1:
-x + 6y = 13
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 3.
To solve the system of equations, we can use the method of substitution.
We start by solving one of the equations for one variable in terms of the other. Let's solve the first equation for x:
-x + 6y = 13
x = 13 - 6y
Now we substitute this expression for x in the second equation:
4(13 - 6y) - 10y = -10
52 - 24y - 10y = -10
52 - 34y = -10
-34y = -62
y = 62/34
y = 31/17
Now we substitute this value of y back into the expression we found for x:
x = 13 - 6(31/17)
x = 221/17 - 186/17
x = 35/17
Therefore, the solution to the system of equations is x = 35/17 and y = 31/17.
To solve the system of equations:
Step 1: Multiply the first equation by 4 to eliminate the x variable.
4(-x+6y) = 4(13)
-4x + 24y = 52
Step 2: Multiply the second equation by -1 to eliminate the x variable.
-1(4x–10y) = -1(–10)
-4x + 10y = 10
Step 3: Add the two equations together to eliminate the x variable.
(-4x + 24y) + (-4x + 10y) = 52 + 10
-8x + 34y = 62
Step 4: Divide every term by -2 to simplify the equation.
-8x/-2 + 34y/-2 = 62/-2
4x - 17y = -31
So, the simplified system of equations is:
4x - 17y = -31
-4x + 10y = 10
Now we can solve this system by either substitution or elimination method.